In finance, a derivative is financial instrument whose return is derived from the performance of an underlying asset or assets. The most common types of derivatives are futures, options, and swaps. Farmers, mortgage lenders, insurance companies, mineral producers, and other entities frequently use derivatives to offload risk. For example, a farmer might sell a futures contract promising to sell a future harvest to a purchaser at a fixed per-bushel price. In this manner, the farmer knows how much he will make per bushel long before that bushel is ever harvested, and protects himself from the risk that market prices for his agricultural product will plummet at harvest time. The purchaser protects itself from the risk that market prices for the agricultural product will spike at harvest time. As another example, a commercial airline might buy an options contract from a jet fuel distributor giving the commercial airline the right to buy a quantity of jet fuel at a future date at a fixed price. In this manner, the commercial airline protects itself from a temporary spike in the price of jet fuel.
Brief Primer on Options
For purposes of brevity, the remainder of this specification will focus on the invention's applicability to options, and especially, on call options. It should be understood, however, that the scope and principles of this invention are not necessarily limited to options or call options, unless and to the extent that the claims expressly limit them to such.
A call option is a financial contract that gives the buyer of the option the right, but not the obligation, to buy an agreed quantity of a particular asset (e.g., shares of stock) from the seller of the option at a certain time for a certain price, called the strike price. A trader who expects a stock price to increase can leverage his bet by buying call options on the stock rather than buying the underlying stock itself.
Conversely, a put option is a financial contract that gives the buyer of the put the right, but not the obligation, to sell an agreed quantity of a particular asset to the seller of the option at a certain time for a certain price (the strike price). A trader who expects a stock's price to decrease can make a bet by buying put options on the stock. The trader's risk is limited to the cost of the put option. By comparison, if the trader chose instead to short-sell the underlying stock, the trader's risk would be potentially unlimited.
How Options are Valued
The market price of a call option reflects the market's assessment of the likelihood that the option will finish “in the money,” that is, that the price of the underlying asset will rise sufficiently to match or exceed the strike price of the call option before or by the time the call option expires. Conceptually, there are two main theoretical components to the price of a call option—the call option's time value and the call option's intrinsic value.
The time value of a call option depends on two factors. The first factor is the volatility of the underlying asset. The more volatile the underlying asset, the more likely that it is to meet or exceed the strike price on the expiration date. Therefore, the more volatile the asset, the greater its time value. The second factor is the time to expiration. The farther away the expiration date is, the more likely that the underlying asset will reach or exceed the call option strike price. Therefore, the time value of an option declines exponentially with time, reaching zero at the expiration date.
The intrinsic value of a call option is the difference between the strike price of the option to the current market value of the underlying asset, also known as the spot price. A call option whose strike price exceeds the spot price is referred to as an out-of-the-money option. An option that expires out-of-the-money expires worthless. The time value of a call option is the difference between the market value of the option and the intrinsic value of the option.
In 1973, two economists developed a complex mathematical formula, known as the Black-Scholes model, for calculating a “theoretically” appropriate price for an equity option. The Black-Scholes equation assumes that the probable future price of an underlying security will follow a normal distribution. Furthermore, the Black Scholes equation assumes that the price of the stock will follow a geometric Brownian motion with constant drift and volatility. The equation also assumes that the price of an option will be a function, in part, of the opportunity cost of investing money into the option. The opportunity cost is the interest that the investor would otherwise earn on the investment had it been invested in a risk-free manner. This opportunity cost is typically modeled as a function of the time to expiration of the option and the prevailing “risk-free” interest rate.
The Black-Scholes model, which is sometimes referred to as the “Fundamental Theorem of Finance,” laid the foundation for the modern, and rapidly growing, derivatives market. The model gave “market makers” a theoretical basis for pricing options and assessing the risk, and potential profits to be earned (based on the bid-ask spread), entailed in creating, buying, and selling options to the public through an exchange.
The Black-Scholes model, however, does not perfectly model the historical patterns of equities prices. For example, U.S. stock prices over much of the 20th century have, on average, appreciated far more rapidly between the months of November and April than between the months of May and October. One would not expect such a persistent asymmetric pattern to emerge from a market whose stock behavior modeled a geometric Brownian motion with constant drift and volatility.
Some experts have surmised that the reason that asymmetrical market return patterns have persisted so long is the difficulty of successfully arbitraging them, given the transaction costs and tax consequences often associated with any arbitrage attempt. If a typical investor annually bought a basket of equities on November 1, and then annually sold that basket on May 1, investing the proceeds in risk-free assets in the months of May through October, that investor would incur the transaction costs associated with buying and selling that basket twice a year, and also annually incur tax liabilities on any realized gains. The transaction costs and tax liabilities are likely to exceed the benefits of following this strategy.
Using Options to Arbitrage Persistent Asymmetrical Market Behaviors
It is one of the objects of this invention to give an investor a derivative-trading strategy for more effectively attempting to leverage persistent asymmetrical market return patterns, such as the one described above. The time value of an option investment is such a large fraction of its overall cost, especially in the case of deep-out-of-the-money options, that an investor can more efficiently attempt to leverage these asymmetrical market patterns by trading in and out of derivatives than by trading in and out of the underlying securities. For example, if an asymmetrical pattern of equity appreciation persists in a market that prices options approximately according to their theoretical, Black-Scholes model, then the investor can arbitrage this pattern by selling call options short at the beginning of a season of historically depressed returns, and closing out the position at or near the end of that season. Likewise, the investor can further arbitrage this pattern by purchasing call options, or selling put options, at the beginning of a season of historically enhanced market performance, and closing out that position at or near the end of that season.
Using Baskets of Options to Diversify Risk
Although an investor could attempt to leverage an asymmetrical market pattern by trading derivatives on a single company's stock, the investor would, by doing so, expose himself to all of the risks associated with that one stock. Therefore, it is another object of this invention to provide customizable strategies for assembling a portfolio of derivatives, such as call options, to more effectively arbitrage the asymmetrical stock performance characteristics of the whole market, or of one or more specific segments (e.g., large, small, growth, or value) or industry sectors within the market, without becoming over-exposed to the peculiar risks associated with any given company.
Long Term Options
In 1990 the Chicago Board Options Exchange introduced long term call options which they referred to as “Long Term Equity Anticipation Securities” or LEAPS® in response to market interest in options with longer term expirations. The Chicago Board's LEAPS have expiration dates up to three years from the date they are issued. They are typically issued with strike prices approximately 25% above or below the price of the underlying stock when the lead was first offered. It is therefore another object of this invention to enable investors to customize strategies for assembling a portfolio of long term options, and especially long term call options.
Trading Platform for Individual Clients
Although the market for derivatives has exploded in recent years, the pool of participants in the derivatives market is still mostly confined to large institutions such as hedge funds, insurance companies, commodities businesses, and banks and other financial institutions. Most discount brokerages do not permit their investors to participate in the option trading market. Furthermore, individual investor interest in derivatives has been largely confined to speculation in individual options.
Therefore, it is yet another object of this invention to provide a trading platform for individual investors that provides customized filters for selecting a portfolio of options using the derivative trading strategies of the present invention.
These and many other embodiments and advantages of the invention will be readily apparent to those skilled in the art from the following detailed description taken in conjunction with the annexed sheets of drawings, which illustrate the invention.